Two stations P and Q are 110 km apart on a straight railway track. One train starts from station P at 7:00 a.m. and travels towards station Q at 20 km/h. Another train starts from station Q at 8:00 a.m. and travels towards station P at 25 km/h. At what time will the two trains meet?

Introduction / Context:
This question is a standard application of the relative speed concept, where two trains start at different times from two stations and travel towards each other. It checks your understanding of how to handle different starting times and how to set up a simple linear equation based on distance, speed, and time.

Given Data / Assumptions:

• Distance between stations P and Q = 110 km.
• Train from P leaves at 7:00 a.m. with speed 20 km/h.
• Train from Q leaves at 8:00 a.m. with speed 25 km/h.
• Both trains travel along the same straight track towards each other.
• We must find the clock time when they meet.

Concept / Approach:
When two objects move towards each other, their relative speed is the sum of their individual speeds, but here they start at different times. The standard method is to measure time from one train's start and adjust for the delayed start of the second train. Let the time in hours from 7:00 a.m. to the meeting instant be t. Then the first train travels for t hours and the second train travels for t minus 1 hours, because it starts one hour later. The sum of their distances will be equal to 110 km.

Step-by-Step Solution:
Step 1: Let t be the time in hours after 7:00 a.m. when the trains meet.Step 2: Distance covered by the first train from P = 20 * t.Step 3: The second train from Q starts at 8:00 a.m., so it travels for (t - 1) hours. Its distance = 25 * (t - 1).Step 4: At the meeting point, total distance covered = 110 km, so 20 * t + 25 * (t - 1) = 110.Step 5: Simplify: 20t + 25t - 25 = 110, giving 45t - 25 = 110, hence 45t = 135 and t = 3 hours.Step 6: Time of meeting = 7:00 a.m. + 3 hours = 10:00 a.m.

Verification / Alternative check:
In three hours, the first train covers 20 * 3 = 60 km.The second train travels for 2 hours (from 8:00 a.m. to 10:00 a.m.) and covers 25 * 2 = 50 km.Total distance = 60 + 50 = 110 km, which matches the distance between the stations.

Why Other Options Are Wrong:
Times like 9:30 a.m. or 9:15 a.m. arise if you incorrectly assume both trains start together or mishandle the one-hour delay. The option 8:45 a.m. is too early, leaving insufficient time for either train to cover the required distances. The option 10:30 a.m. would cause the trains to cover more than 110 km combined, implying they would have already met earlier.

Common Pitfalls:
Many candidates forget to account for the late start of the second train and treat the problem as if both trains started at 7:00 a.m. Another frequent error is to use relative speed directly without adjusting time, which works only when starting times are the same. Correctly defining the variable t and writing the distance equation is the safest way to avoid confusion.

Final Answer:
The two trains will meet at 10:00 a.m.